Question

In a large city, the heights of 10-year-old children are approximately normally distributed with a mean of 53.7 inches and standard deviation of 3.7 inches.

(a) What is the probability that a randomly chosen 10-year-old child has a height that is less than than 50.35 inches? Round your answer to 3 decimal places.



(b) What is the probability that a randomly chosen 10-year-old child has a height that is more than 53.2 inches? Round your answer to 3 decimal places.

Answer 1

x : the heights of 10-year-old children

mean = 53.7 inches

standard deviation =  3.7 inches.

(a)

P( height that is less than than 50.35 inches ) = P ( x < 50.35 )

= P ((x - 53.7)/3.7 < (50.35 - 53.7)/3.7 )

= P (z< -0.9054 )

= NORMSDIST(-0.9054)

= 0.183

Answer : 0.183

P( height that is more than 53.2 inches ) = P ( x > 53.2 )

= P ((x - 53.7)/3.7 > (53.2 - 53.7)/3.7 )

= P (z > -0.1351 )

= 1 - NORMSDIST(-0.1351)

= 0.554

Answer : 0.554